This notebook reads in results for the MultiBLUP model using 5000 random gene group to do the following:
- summarize the number of models that pass filtering criteria
- examine the distribution of the likelihood ratio (see Edwards et al 2016)
- establish 95 percentiles for heritability and the likelihood ratio
knitr::opts_knit$set(root.dir = "~/Documents/AA-GenomicPrediction/",
warning = FALSE)
knitr::opts_chunk$set(fig.width = 10)
library(tidyverse)
library(knitr)
library(kableExtra)
library(quantreg)
library(data.table)
library(viridis)
library(emdbook)
library(gridExtra)
library(cowplot)
Size distribution of null pathways
Number of markers should have a uniform distribution
aa_fam <- read.csv("data/processed/aa_family_ids.csv",
header = TRUE)
null_dist <- read_csv("reports/lr_null_results.csv") %>%
# set amino acid family ids
left_join(., aa_fam, by = "trait")
null_dist %>%
distinct(pathway, size.x) %>%
ggplot(., aes(size.x)) +
geom_histogram(binwidth = 1000) +
xlab("Gene group size (number of SNPs)")

Filtering
Filter out values where the REML model did not converge
Set negative heritability estimates to zero
Export summary to S2 table
S2table <- null_dist %>%
group_by(trait) %>%
filter(Component %in% "Share_K1") %>%
mutate("Number of gene groups" = ifelse(SD < 0 | LR < 0, 0, 1),
"Failed to converge" = ifelse(SD < 0, 1, 0),
"Negative LR" = ifelse(LR < 0, 1, 0)) %>%
select("Number of gene groups", "Failed to converge", "Negative LR") %>%
summarize_all(.funs = "sum")
Adding missing grouping variables: `trait`
S2table %>%
write_csv(., "reports/tableS2_null_summary.csv")
head(S2table)
Apply filters to null distribution
null_dist <- null_dist %>%
# mutate(Share = ifelse(Share < 0, 0, Share),
# Share = ifelse(Share > 1, 1, Share)) %>%
rename(size = "size.x",
n_genes = "n_genes.x") %>%
# remove values where SD of heritability is strange (results in inflated LR)
filter(# SD > 0 & LR >= 0 &
Component %in% "Share_K1") %>%
dplyr::select(family, trait, pathway, size, n_genes, group_size, LR, Component, Share, SD)
head(null_dist)
Likelihood ratio
Distribution
Expect LR to be distributed as \(\chi^2_{df 1}\)~ based on Wilks’ Theorem
null_dist %>%
ggplot(., aes(LR)) +
geom_histogram(bins = 50) +
facet_wrap(~trait, scales = "free", ncol = 6) +
theme_bw()

# ggsave("reports/figures/null_histogram.png", height = 12, width = 8)
QQ plots
Maybe some inflation at smaller group sizes (< 10,000 SNPs)
null_dist %>%
# filter(trait %in% c("ala", "ala_PyrFam", "asp_t", "his", "Total")) %>%
mutate(group_size = fct_relevel(group_size, "[0,10000]")) %>%
ggplot(., aes(sample = LR, colour = group_size)) +
scale_colour_manual(values = viridis(6)[1:5]) +
stat_qq(distribution = qchisq, dparams = list(df = 1.5)) +
facet_wrap( ~ trait, scales = "free", ncol = 6) +
geom_abline(slope = 1, intercept = 0) +
theme_bw() +
theme(legend.position = "top")

# ggsave("reports/figures/FigS5.png", height = 12, width = 8)
LR goodness-of-fit tests
Test if LR follows Wilks’ theorem expectation of \(\chi^2\) distribution
- \(\chi^2\) test
- Kolmogorov-Smirnov test (D)
GoF <- null_dist %>%
select(trait, LR) %>%
group_by(trait) %>%
mutate(
# return distance (D) for Kolmogorov-Smirnov goodness-of-fit test
# df = 1
D1 = ks.test(LR, pchisq, df = 1)$statistic,
# df = mixture of 1 and 2
D1_2 = ks.test(LR, rchibarsq(length(LR), 2, mix = 0.5))$statistic,
# df = 2
D2 = ks.test(LR, pchisq, df = 2)$statistic,
# return p-value for chi-sq goodness of fit test
# df = 1
X2_1 = suppressWarnings(chisq.test(LR, rchisq(length(LR), 1))$p.value),
# df = mixture of 1 and 2
X2_1_2 = suppressWarnings(chisq.test(LR, rchibarsq(length(LR), 2, mix = 0.5))$p.value),
# df = 2
X2_2 = suppressWarnings(chisq.test(LR, rchisq(length(LR), 2))$p.value)) %>%
summarise_all(mean) %>%
select(trait, LR, D1, D1_2, D2, X2_1, X2_1_2, X2_2)
# return table of results
GoF %>%
kable(digits = 4) %>%
kable_styling(bootstrap_options = "striped")
| trait |
LR |
D1 |
D1_2 |
D2 |
X2_1 |
X2_1_2 |
X2_2 |
| ala |
0.7433 |
0.0998 |
0.2528 |
0.4018 |
0.2821 |
0.2821 |
0.2821 |
| ala_PyrFam |
3.6045 |
0.7322 |
0.6888 |
0.6492 |
0.2741 |
0.2741 |
0.2741 |
| ala_t |
1.0870 |
0.0310 |
0.1540 |
0.3021 |
0.2731 |
0.2731 |
0.2731 |
| arg |
1.4788 |
0.2762 |
0.1274 |
0.1341 |
0.2631 |
0.2631 |
0.2631 |
| arg_GluFam |
0.3714 |
0.2746 |
0.4298 |
0.5769 |
0.2997 |
0.2997 |
0.2997 |
| arg_t |
0.5028 |
0.1906 |
0.3290 |
0.4820 |
0.2879 |
0.2879 |
0.2879 |
| asp |
0.6665 |
0.1086 |
0.2638 |
0.4059 |
0.2827 |
0.2827 |
0.2827 |
| asp_AspFam |
1.7296 |
0.2077 |
0.0846 |
0.1587 |
0.2611 |
0.2611 |
0.2611 |
| asp_t |
1.7883 |
0.5250 |
0.3986 |
0.2375 |
0.2666 |
0.2666 |
0.2666 |
| AspFam |
0.6107 |
0.1367 |
0.2860 |
0.4300 |
0.2856 |
0.2856 |
0.2856 |
| AspFam_Asp |
1.6519 |
0.1948 |
0.0866 |
0.1760 |
0.2620 |
0.2620 |
0.2620 |
| BCAA |
0.5036 |
0.1833 |
0.3398 |
0.4773 |
0.2855 |
0.2855 |
0.2855 |
| gln |
0.4680 |
0.2112 |
0.3460 |
0.5012 |
0.2872 |
0.2872 |
0.2872 |
| gln_GluFam |
0.3530 |
0.3207 |
0.4626 |
0.6198 |
0.3076 |
0.3076 |
0.3076 |
| gln_t |
0.3872 |
0.2956 |
0.4464 |
0.5948 |
0.3045 |
0.3045 |
0.3045 |
| glu |
0.4454 |
0.2118 |
0.3526 |
0.5077 |
0.2893 |
0.2893 |
0.2893 |
| glu_GluFam |
0.4530 |
0.2315 |
0.3810 |
0.5324 |
0.2956 |
0.2956 |
0.2956 |
| glu_t |
0.9756 |
0.0514 |
0.1918 |
0.3478 |
0.2776 |
0.2776 |
0.2776 |
| GluFam |
0.7638 |
0.1049 |
0.2222 |
0.3325 |
0.2718 |
0.2718 |
0.2718 |
| GluFam_glu |
0.4788 |
0.2183 |
0.3710 |
0.5199 |
0.2935 |
0.2935 |
0.2935 |
| gly |
0.4790 |
0.2193 |
0.3564 |
0.5036 |
0.2823 |
0.2823 |
0.2823 |
| gly_SerFam |
0.3489 |
0.2950 |
0.4408 |
0.5970 |
0.3020 |
0.3020 |
0.3020 |
| gly_t |
0.2541 |
0.3801 |
0.5304 |
0.6819 |
0.3093 |
0.3093 |
0.3093 |
| his |
3.2382 |
0.5027 |
0.4780 |
0.4588 |
0.2677 |
0.2677 |
0.2677 |
| his_GluFam |
1.0107 |
0.0314 |
0.1876 |
0.3334 |
0.2752 |
0.2752 |
0.2752 |
| his_t |
0.7742 |
0.0967 |
0.2296 |
0.3924 |
0.2804 |
0.2804 |
0.2804 |
| ile |
0.5745 |
0.1624 |
0.3138 |
0.4646 |
0.2866 |
0.2866 |
0.2866 |
| ile_AspFam |
0.6032 |
0.1544 |
0.3024 |
0.4568 |
0.2872 |
0.2872 |
0.2872 |
| ile_BCAA |
3.1959 |
0.6695 |
0.6028 |
0.5313 |
0.2671 |
0.2671 |
0.2671 |
| ile_t |
0.8015 |
0.0837 |
0.2388 |
0.3824 |
0.2814 |
0.2814 |
0.2814 |
| leu |
0.5778 |
0.1496 |
0.2926 |
0.4426 |
0.2843 |
0.2843 |
0.2843 |
| leu_BCAA |
0.7253 |
0.0989 |
0.2604 |
0.3997 |
0.2830 |
0.2830 |
0.2830 |
| leu_PyrFam |
1.1848 |
0.1292 |
0.1300 |
0.2752 |
0.2714 |
0.2714 |
0.2714 |
| leu_t |
0.9978 |
0.0251 |
0.1642 |
0.3169 |
0.2748 |
0.2748 |
0.2748 |
| lys |
0.6401 |
0.1277 |
0.2592 |
0.3825 |
0.2787 |
0.2787 |
0.2787 |
| lys_AspFam |
3.0090 |
0.6554 |
0.5930 |
0.5343 |
0.2718 |
0.2718 |
0.2718 |
| lys_t |
0.4535 |
0.2243 |
0.3788 |
0.5265 |
0.2934 |
0.2934 |
0.2934 |
| met |
0.5487 |
0.1559 |
0.2996 |
0.4417 |
0.2834 |
0.2834 |
0.2834 |
| met_AspFam |
-6.3774 |
0.9996 |
0.9996 |
0.9996 |
0.2861 |
0.2861 |
0.2861 |
| met_t |
0.5298 |
0.1675 |
0.3168 |
0.4633 |
0.2865 |
0.2865 |
0.2865 |
| phe |
0.9022 |
0.0539 |
0.2036 |
0.3560 |
0.2788 |
0.2788 |
0.2788 |
| phe_ShikFam |
0.4992 |
0.1990 |
0.3444 |
0.4984 |
0.2903 |
0.2903 |
0.2903 |
| phe_t |
1.0603 |
0.0216 |
0.1622 |
0.3115 |
0.2730 |
0.2730 |
0.2730 |
| pro |
0.4705 |
0.1964 |
0.3382 |
0.4860 |
0.2889 |
0.2889 |
0.2889 |
| pro_GluFam |
0.5255 |
0.1719 |
0.2962 |
0.4496 |
0.2829 |
0.2829 |
0.2829 |
| pro_t |
0.4862 |
0.1919 |
0.3382 |
0.4794 |
0.2871 |
0.2871 |
0.2871 |
| PyrFam |
0.5045 |
0.1926 |
0.3556 |
0.4928 |
0.2909 |
0.2909 |
0.2909 |
| ser |
0.4128 |
0.2313 |
0.3884 |
0.5297 |
0.2930 |
0.2930 |
0.2930 |
| ser_SerFam |
0.4666 |
0.2395 |
0.3872 |
0.5395 |
0.2989 |
0.2989 |
0.2989 |
| ser_t |
0.4228 |
0.2611 |
0.4080 |
0.5560 |
0.3015 |
0.3015 |
0.3015 |
| SerFam |
0.5007 |
0.2011 |
0.3414 |
0.4788 |
0.2827 |
0.2827 |
0.2827 |
| ShikFam |
1.6064 |
0.1484 |
0.0436 |
0.1879 |
0.2628 |
0.2628 |
0.2628 |
| thr |
1.4055 |
0.1325 |
0.0666 |
0.2166 |
0.2657 |
0.2657 |
0.2657 |
| thr_AspFam |
0.7956 |
0.0949 |
0.2530 |
0.3914 |
0.2817 |
0.2817 |
0.2817 |
| total |
0.5574 |
0.1456 |
0.2850 |
0.4249 |
0.2818 |
0.2818 |
0.2818 |
| trp |
0.6488 |
0.1471 |
0.2976 |
0.4487 |
0.2861 |
0.2861 |
0.2861 |
| trp_ShikFam |
0.4828 |
0.2035 |
0.3354 |
0.4928 |
0.2859 |
0.2859 |
0.2859 |
| trp_t |
0.5313 |
0.1832 |
0.3136 |
0.4585 |
0.2813 |
0.2813 |
0.2813 |
| tyr |
0.5001 |
0.1823 |
0.3240 |
0.4780 |
0.2882 |
0.2882 |
0.2882 |
| tyr_ShikFam |
0.4890 |
0.1888 |
0.3278 |
0.4752 |
0.2862 |
0.2862 |
0.2862 |
| tyr_t |
0.8177 |
0.0762 |
0.2144 |
0.3606 |
0.2811 |
0.2811 |
0.2811 |
| val |
0.6674 |
0.1248 |
0.2408 |
0.3726 |
0.2748 |
0.2748 |
0.2748 |
| val_BCAA |
1.3624 |
0.4419 |
0.2864 |
0.2004 |
0.2746 |
0.2746 |
0.2746 |
| val_PyrFam |
0.6507 |
0.1195 |
0.2688 |
0.4137 |
0.2829 |
0.2829 |
0.2829 |
| val_t |
0.3689 |
0.2647 |
0.4112 |
0.5667 |
0.2959 |
0.2959 |
0.2959 |
# plot results
GoF %>%
select(trait, D1, D1_2, D2) %>%
gather(key = df, value = D, -trait) %>%
mutate(df = recode(df, D1 = "1", D1_2 = "1.5", D2 = "2")) %>%
ggplot(., aes(df, D, group = trait)) +
geom_point() +
geom_line() +
xlab("degrees of freedom") +
ylab("Kolmogorov-Smirnov test statistic (D)") +
facet_wrap(~ trait, scales = "fixed", ncol = 6) +
theme_bw() +
theme(legend.position = "none")

# ggsave("reports/figures/FigS4.png", height = 12, width = 10)
GoF %>%
select(trait, D1, D1_2, D2) %>%
gather(key = df, value = D, -trait) %>%
group_by(trait) %>%
mutate(df = recode(df, D1 = "1", D1_2 = "1.5", D2 = "2")) %>%
slice(which.min(D)) %>%
ungroup() %>%
write_csv("reports/goodness_of_fit.csv") %>%
head()
Empirical thresholds
95 percentile for LR
Fit an additive quantile regression to establish 95 percentile cut off for LR at different pathway sizes (number of markers)
## 95% LR threshold for plotting
lr_fit <- NULL
coefs <- NULL
for (i in unique(null_dist$trait)) {
lr_fit[[i]] <- rqss(as.numeric(LR) ~ qss(size, constraint = "I"),
data = null_dist[null_dist$trait==i,], tau = 0.95)
coefs[[i]] <- data.frame(lr_fit[[i]]$qss$size$xyz) %>%
mutate(lr_95 = X2 + lr_fit[[i]]$coef[1],
size = X1) %>%
dplyr::select(size, lr_95)
}
lr_threshold <- rbindlist(coefs, idcol = "trait")
null_dist <- null_dist %>%
left_join(., lr_threshold, by = c("trait", "size")) %>%
mutate(col = LR >= lr_95)
null_dist %>%
as_tibble() %>%
head()
95 percentile for \(h^2\)
Fit an additive quantile regression to establish 95% quantile cut off for proportion of genomic variance explained (H^2) at different pathway sizes (number of markers)
h2_fit <- NULL
h2_coefs <- NULL
for (i in unique(null_dist$trait)) {
h2_fit[[i]] <- rqss(as.numeric(Share) ~ qss(size, constraint = "I"),
data = null_dist[null_dist$trait==i,], tau = 0.977) #FDR corrected
# data = null_dist[null_dist$trait==i,], tau = 0.95)
h2_coefs[[i]] <- data.frame(h2_fit[[i]]$qss$size$xyz) %>%
mutate(h2_95 = X2 + h2_fit[[i]]$coef[1],
size = X1) %>%
dplyr::select(size, h2_95)
}
h2_threshold <- rbindlist(h2_coefs, idcol = "trait") %>%
as_tibble()
head(h2_threshold)
Plot null distribution
Blue dots are pathways that also pass the LR_95 threshold
Solid line is the 95% percentile for proportion of heritability explained
Dashed line is the infinitesimal expectation (each SNP contributes approximately equal amount of variation)

save results
save(lr_fit, h2_fit, file = "reports/null_distribution.RData")
Error in save(lr_fit, h2_fit, file = "reports/null_distribution.RData") :
object ‘h2_fit’ not found
---
title: "AA-GP: process null distribution"
output: 
  html_notebook:
    toc: yes
    toc_float: yes
    code_folding: hide
date: "`r format(Sys.time(), '%d %B, %Y')`"
editor_options: 
  chunk_output_type: inline
---

This notebook reads in results for the MultiBLUP model using 5000 random gene group to do the following:   

* summarize the number of models that pass filtering criteria   
* examine the distribution of the likelihood ratio (see Edwards et al 2016)   
* establish 95 percentiles for heritability and the likelihood ratio  

```{r setup, results = "hide"}
knitr::opts_knit$set(root.dir = "~/Documents/AA-GenomicPrediction/",
                     warning = FALSE)
knitr::opts_chunk$set(fig.width = 10)

library(tidyverse)
library(knitr)
library(kableExtra)
library(quantreg)
library(data.table)
library(viridis)
library(emdbook)
library(gridExtra)
library(cowplot)
```

# Size distribution of null pathways
Number of markers should have a uniform distribution

```{r load data, fig.width = 5, results = "hide"} 
aa_fam <- read.csv("data/processed/aa_family_ids.csv",
                   header = TRUE)

null_dist <- read_csv("reports/lr_null_results.csv") %>%
  # set amino acid family ids 
  left_join(., aa_fam, by = "trait")

null_dist %>%
  distinct(pathway, size.x) %>%
  ggplot(., aes(size.x)) +
  geom_histogram(binwidth = 1000) +
  xlab("Gene group size (number of SNPs)")
```

# Filtering
Filter out values where the REML model did not converge  

Set negative heritability estimates to zero 

Export summary to S2 table

```{r table S2}
S2table <- null_dist %>%
  group_by(trait) %>%
  filter(Component %in% "Share_K1") %>%
  mutate("Number of gene groups" = ifelse(SD < 0 | LR < 0, 0, 1),
         "Failed to converge" = ifelse(SD < 0, 1, 0),
         "Negative LR" = ifelse(LR < 0, 1, 0)) %>%
  select("Number of gene groups", "Failed to converge", "Negative LR") %>%
  summarize_all(.funs = "sum") 

S2table %>%
  write_csv(., "reports/tableS2_null_summary.csv")

head(S2table)
```

Apply filters to null distribution 

```{r filter null}
null_dist <- null_dist %>% 
  # mutate(Share = ifelse(Share < 0, 0, Share),
  #        Share = ifelse(Share > 1, 1, Share)) %>%
  rename(size = "size.x",
         n_genes = "n_genes.x") %>% 
  # remove values where SD of heritability is strange (results in inflated LR)
  filter(# SD > 0 & LR >= 0 &
    Component %in% "Share_K1") %>%
  dplyr::select(family, trait, pathway, size, n_genes, group_size, LR, Component, Share, SD) 

head(null_dist)
```

# Likelihood ratio

## Distribution
Expect LR to be distributed as $\chi^2_{df 1}$~ based on Wilks' Theorem 

```{r null lr distribution, fig.height = 14, fig.width = 8}
null_dist %>%
    ggplot(., aes(LR)) + 
    geom_histogram(bins = 50) +
  facet_wrap(~trait, scales = "free", ncol = 6) +
  theme_bw() 

# ggsave("reports/figures/null_histogram.png", height = 12, width = 8)
```

## QQ plots

Maybe some inflation at smaller group sizes (< 10,000 SNPs)

```{r qqchisq, fig.height = 14, fig.width = 8}
null_dist %>%
  # filter(trait %in% c("ala", "ala_PyrFam", "asp_t", "his", "Total")) %>% 
  mutate(group_size = fct_relevel(group_size, "[0,10000]")) %>%
  ggplot(., aes(sample = LR, colour = group_size)) + 
  scale_colour_manual(values = viridis(6)[1:5]) + 
  stat_qq(distribution = qchisq, dparams = list(df = 1.5)) +
  facet_wrap( ~ trait, scales = "free", ncol = 6) +
  geom_abline(slope = 1, intercept = 0) +
  theme_bw() + 
  theme(legend.position = "top") 

# ggsave("reports/figures/FigS5.png", height = 12, width = 8)
```

## LR goodness-of-fit tests 
Test if LR follows Wilks' theorem expectation of $\chi^2$ distribution   

* $\chi^2$ test    
* Kolmogorov-Smirnov test (D)  

```{r test goodness of fit, results = "hide", message = FALSE}
GoF <- null_dist %>% 
  select(trait, LR) %>%
  group_by(trait) %>%
  mutate(
    # return distance (D) for Kolmogorov-Smirnov goodness-of-fit test 
    # df = 1
    D1 = ks.test(LR, pchisq, df = 1)$statistic,
    # df = mixture of 1 and 2 
    D1_2 = ks.test(LR, rchibarsq(length(LR), 2, mix = 0.5))$statistic,
    # df = 2
    D2 = ks.test(LR, pchisq, df = 2)$statistic,
    # return p-value for chi-sq goodness of fit test 
    # df = 1
    X2_1 = suppressWarnings(chisq.test(LR, rchisq(length(LR), 1))$p.value),
    # df = mixture of 1 and 2
    X2_1_2 = suppressWarnings(chisq.test(LR, rchibarsq(length(LR), 2, mix = 0.5))$p.value),
    # df = 2
    X2_2 = suppressWarnings(chisq.test(LR, rchisq(length(LR), 2))$p.value)) %>%
  summarise_all(mean) %>%
  select(trait, LR, D1, D1_2, D2, X2_1, X2_1_2, X2_2)
```

```{r gof table}
# return table of results 
GoF %>% 
  kable(digits = 4) %>%
  kable_styling(bootstrap_options = "striped")
```

```{r plot KS statistic, fig.height = 14, fig.width = 8}
# plot results
GoF %>%
  select(trait, D1, D1_2, D2) %>%
  gather(key = df, value = D, -trait) %>%
  mutate(df = recode(df, D1 = "1", D1_2 = "1.5", D2 = "2")) %>%
  ggplot(., aes(df, D, group = trait)) +
  geom_point() + 
  geom_line() +
  xlab("degrees of freedom") +
  ylab("Kolmogorov-Smirnov test statistic (D)") + 
  facet_wrap(~ trait, scales = "fixed", ncol = 6) +
  theme_bw() +
  theme(legend.position = "none")

# ggsave("reports/figures/FigS4.png", height = 12, width = 10)  
```

```{r get minimum D value}
GoF %>%
  select(trait, D1, D1_2, D2) %>%
  gather(key = df, value = D, -trait) %>%
  group_by(trait) %>%
  mutate(df = recode(df, D1 = "1", D1_2 = "1.5", D2 = "2")) %>%
  slice(which.min(D)) %>%
  ungroup() %>%
  write_csv("reports/goodness_of_fit.csv") %>%
  head()
```

# Empirical thresholds

## 95 percentile for LR 

Fit an additive quantile regression to establish 95 percentile cut off for LR at different pathway sizes (number of markers) 

```{r 95 quantile for LR}
## 95% LR threshold for plotting
lr_fit <- NULL
coefs <- NULL

for (i in unique(null_dist$trait)) {
  lr_fit[[i]] <- rqss(as.numeric(LR) ~ qss(size, constraint = "I"), 
                      data = null_dist[null_dist$trait==i,], tau = 0.95) 
  coefs[[i]] <- data.frame(lr_fit[[i]]$qss$size$xyz) %>%
    mutate(lr_95 = X2 + lr_fit[[i]]$coef[1],
           size = X1) %>%
    dplyr::select(size, lr_95)
}

lr_threshold <- rbindlist(coefs, idcol = "trait")

null_dist <- null_dist %>%
  left_join(., lr_threshold, by = c("trait", "size")) %>%
  mutate(col = LR >= lr_95) 

null_dist %>%
  as_tibble() %>%
  head()
```

## 95 percentile for $h^2$ 

Fit an additive quantile regression to establish 95% quantile cut off for proportion of genomic variance explained (H^2) at different pathway sizes (number of markers) 

```{r 95 quantile for H2}
h2_fit <- NULL
h2_coefs <- NULL

for (i in unique(null_dist$trait)) {
  h2_fit[[i]] <- rqss(as.numeric(Share) ~ qss(size, constraint = "I"), 
                      data = null_dist[null_dist$trait==i,], tau = 0.977) #FDR corrected 
                      # data = null_dist[null_dist$trait==i,], tau = 0.95)
  h2_coefs[[i]] <- data.frame(h2_fit[[i]]$qss$size$xyz) %>%
    mutate(h2_95 = X2 + h2_fit[[i]]$coef[1],
           size = X1) %>%
    dplyr::select(size, h2_95)
}

h2_threshold <- rbindlist(h2_coefs, idcol = "trait") %>%
  as_tibble()
  
head(h2_threshold)
```

## Plot null distribution
Blue dots are pathways that also pass the LR_95 threshold  
Solid line is the 95% percentile for proportion of heritability explained  
Dashed line is the infinitesimal expectation (each SNP contributes approximately equal amount of variation)

```{r h2 95 threshold, fig.height = 14, fig.width = 8}
null_dist %>%
  ggplot(., aes(size, Share, colour = col)) +
  scale_colour_manual(values = c("lightgrey", "#1c9099"),
                      labels = c(expression(paste(LR < LR[95])), 
                                 expression(paste(LR > LR[95])))) + 
  geom_point(position = position_dodge(width = 0.3), aes(size = col), alpha = 0.75) + 
  scale_size_manual(guide = "none", values = c(0.1, 0.5)) + 
  geom_quantile(method = "rqss", lambda = 500, quantiles = c(0.95),
                formula = as.formula(y ~ qss(x, constraint = "I")),
                aes(linetype = factor(..quantile..)),
                colour = "black", show.legend = FALSE) + 
  geom_abline(aes(intercept = 0, slope = 1/199452, linetype = "dashed")) + 
  scale_linetype_manual(labels = c(expression(paste(H[95]^2)), 
                                   "infinitesimal"),
                        values = c(1,2)) +
  facet_wrap( ~ trait, ncol = 6) +
  xlim(0, 50000) + 
  theme_bw() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1),
        legend.title = element_blank(),
        legend.text.align = 0)

# ggsave("reports/figures/S2Fig.tiff", height = 12, width = 10)  
```

# save results
```{r save results}
save(lr_fit, h2_fit, file = "reports/null_distribution.RData")
```
